Python 归递 with Decorator 修饰器

Just found out that comments in 优快云 does not work for me, and others:

https://blog.youkuaiyun.com/qq_33696345/article/details/87894969

https://blog.youkuaiyun.com/tangdou5682/article/details/52351604

no matter how I change my browser window size. I tried Chrome and Firefox. So I post comments as seperate posts.

Anyway, here is the topic for today:

https://blog.youkuaiyun.com/CxsGhost/article/details/104150547

In recursion, This is

F(N) = F(N-1) + F(N-3)

换言之，今年牛数等于去年牛数加上新生牛数（新生牛数 = 去年3岁小牛数量=4年前牛数）

计算机归递是双刃剑，是好消息也是坏消息。

In Python,

def cows(n):
    # non cached version
    if n < 4:
        return n

    return cows(n-1) + cows(n-3)

结果是

import cProfile

cProfile.run('print([cows(n) for n in range(40)])')

[0, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 
5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 
1243524, 1822473, 2670964]
         7828941 function calls (45 primitive calls) in 1.829 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000    1.829    1.829 <string>:1(<listcomp>)
        1    0.000    0.000    1.829    1.829 <string>:1(<module>)
7828936/40    1.829    0.000    1.829    0.046 cow.py:5(cows)
        1    0.000    0.000    1.829    1.829 {built-in method builtins.exec}
        1    0.000    0.000    0.000    0.000 {built-in method builtins.print}
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

 毛病是这个函数被调用了7828941次。换句话说我们重复计算了很多次。通过缓存我们可以减少这些计算

from functools import lru_cache as cached

@cached(maxsize=None, typed=False)
def cows_c(n):
    # cached version
    if n < 4:
        return n

    return cows_c(n-1) + cows_c(n-3)

cProfile.run('print([cows_c(n) for n in range(40)])')

         45 function calls in 0.000 seconds

   Ordered by: standard name

   ncalls  tottime  percall  cumtime  percall filename:lineno(function)
        1    0.000    0.000    0.000    0.000 <string>:1(<listcomp>)
        1    0.000    0.000    0.000    0.000 <string>:1(<module>)
       40    0.000    0.000    0.000    0.000 cow.py:13(cows_c)
        1    0.000    0.000    0.000    0.000 {built-in method builtins.exec}
        1    0.000    0.000    0.000    0.000 {built-in method builtins.print}
        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

这个想法是很重要的，因为可以沿着这个想法扩充出去发展成很有用的库，比如不用in process缓存，用分布式缓存，再比如加上函数参数的管理形成context computing。

十年前在Python 2上写过一个版本，时间太长了。